Hello!
We don't offer an API that does that at the moment, sorry. There are two things you could try though:
To identify tracks, chop up the DJ set into ~20 second chunks. Send those chunks to one of our fingerprinters, and then parse the results. You'll get lots of entries for Track 1, then some weirdness where the mix happens, then lots of entries for Track 2, and so on.
Alternatively, you could use the Python version of Echo Nest Remix, analyze the DJ set, segment it by section, and then fingerprint those sections. You may want to do it in smaller (5 to 15 minute?) chunks though, rather than analyzing the entire DJ set at once.
Best, Thor